Table of Dirichlet L-Series and Prime Zeta Modulo Functions for Small Moduli

Abstract

The Dirichlet characters of reduced residue systems modulo m are tabulated for moduli m <= 195. The associated L-series are tabulated for m <= 14 and small positive integer argument s accurate to 10^(-50), their first derivatives for m <= 6. Restricted summation over primes only defines Dirichlet Prime L-functions which lead to Euler products (Prime Zeta Modulo functions). Both are materialized over similar ranges of moduli and arguments. Formulas and numerical techniques are well known; the aim is to provide direct access to reference values.

Table extended to cover moduli <= 195 in the ancillary directory

References in corpus (4)

• An efficient algorithm for accelerating the convergence of oscillatory series, useful for computing the polylogarithm and Hurwitz zeta functions
• On the constant in the Mertens product for arithmetic progressions. II. Numerical values
• Series of Reciprocal Powers of k-almost Primes
• Hardy-Littlewood Constants Embedded into Infinite Products over All Positive Integers

Cited by in corpus (3)

• Survey of Dirichlet Series of Multiplicative Arithmetic Functions
• Summatory relations and prime products for the Stieltjes constants, and other related results
• A von Staudt-type formula for $\sum _{z\in {\mathbb{Z}}_n[i]}{z}^k$